A Review of Lattice Theory for Lyotropic Liquid Crystalline Polymers, Spinodal Decomposition, and Gel Formation

Abstract

Polymer chain conformations can be described by many models. Some of the main ones are shown in Fig. 1. The rod-like model describes polymer molecules as rigid cylinders with high axis ratio. The axis ratio, X, is equal to the length of the polymer divided by the diameter. X = L/d for molecules in any conformation. Linear polymer chains that are not completely rod-like can be described by Kuhn chains, worm-like chains, or segmented rod-like and random coil chains. Kuhn chains are characterized by rigid segments connected by universal joints. The rod-like segment, known as the Kuhn segment, has a characteristic length, 2q. Worm-like chains have continuous deviation from rod-like behavior but are not necessarily completely flexible. The worm-like chains are characterized by a persistence length, q. Polymers of types a-d in Fig. 1 can all form liquid crystalline solutions under appropriate conditions. The final type of chain, the random coil, is not expected to form liquid crystalline solutions.